The 1882-O/S Morgan Silver Dollar is a coin that is notable for its unique mintmark variety, known as the "O/S" variety. This variety is characterized by a re-punched mintmark where the initial "O" mintmark was punched over an earlier punched "S" mintmark. This error occurred during the minting process, resulting in the combination of the two mintmark letters.
 
The term "VAM" stands for Van Allen-Mallis, which refers to a comprehensive cataloging system for Morgan and Peace silver dollars, created by Leroy Van Allen and A. George Mallis. VAM varieties are identified based on specific die variations, die clashes, and other distinguishing features. VAM-5 is one of the cataloged varieties that corresponds to specific characteristics on the coin, such as die markings, doubling, or other anomalies.
 
In the context of your question, "XF45" refers to the coin's grade according to the Sheldon Coin Grading Scale. "XF" stands for Extremely Fine, indicating that the coin has moderate wear but still retains a considerable amount of detail. The numerical grade of "45" further refines the condition assessment, with a higher number indicating a better-preserved coin.
 
"NGC" stands for Numismatic Guaranty Corporation, which is a reputable third-party coin grading service. Having a coin certified by a respected grading service like NGC adds a level of authenticity and provides potential buyers or collectors with assurance of the coin's condition and authenticity.
 
The "TOP 100" designation might refer to the coin's inclusion in a list of the top 100 VAM varieties, highlighting its significance and desirability among collectors.
In summary, the 1882 O/S Morgan Silver Dollar TOP 100 VAM-5 BROKEN S XF45 NGC is a specific variety of coin with a distinct mintmark error, a recognized cataloged variety, and a grade of Extremely Fine 45 as determined by NGC. It's a coin with historical and numismatic value due to its unique characteristics and potential rarity.